[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 5 from proof long-mod-pos-high (previous step)

0 < j % 18446744073709551616, 0 ≤ j, 9223372036854775807 < j % 18446744073709551616 ⊦ j % 18446744073709551616 = cast(64, j) + 18446744073709551616

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
0 ≤ j, 2 ^ (i - 1) - 1 < j % 2 ^ i, 0 < i ⊦ cast(i, j) = j % 2 ^ i - 2 ^ i

Rule argument

seq: 0 ≤ j, 2 ^ (i - 1) - 1 < j % 2 ^ i, 0 < i ⊦ cast(i, j) = j % 2 ^ i - 2 ^ i subst: [j, i] → [j, 64] rotate: F spec: intops inst: name: cast-mod-pos-high

Additional information

Used simplifier rules: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j, 64